Finite Group Databasebeta

← Group #285751

Character table — Group #285751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444888888888888888822444444488888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-11
χ1111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-11111-1-11111-1-1-11
χ1211111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1111-1
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-111-1-1111-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111111111-1-111-1-1-11
χ172222222222222-2-2-2222-2-2-222-2-2000000000000000022-2-2-2-2-22200000000000000000000000000
χ182222222222222-2-2-2222-2-2-222-2-20000000000000000-2-2-22222-2-200000000000000000000000000
χ19222222222222-2222-2-2-22-2-2-2-222222222220000000000-2000000-2-2-2-20000000000000000000000
χ20222222222222-2222-2-2-22-2-2-2-222-2-2-2-2-2-2-2-20000000000-200000022220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i0020000000000000000002i2i−2i−2i0000000000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i002000000000000000000−2i−2i2i2i0000000000
χ2322222222-2-2-2-22-2-2-2222-2-2-2-2-222000000000000000022222-2-2-2-200000000000000000000000000
χ2422222222-2-2-2-22-2-2-2222-2-2-2-2-2220000000000000000-2-22-2-2222200000000000000000000000000
χ2522222222-2-2-2-2-2222-2-2-22-2-222-2-22222-2-2-2-200000000002000000-2-2220000000000000000000000
χ2622222222-2-2-2-2-2222-2-2-22-2-222-2-2-2-2-2-222220000000000200000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i00-2000000000000000000−2i−2i2i2i0000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i00-20000000000000000002i2i−2i−2i0000000000
χ29222-2-2-22-222-2-22000-2-220002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-2000002-2i2−i2i2−i200000000i2−i2i2−i20000000000
χ30222-2-2-22-222-2-22000-2-220002-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-2200000-22i2−i2i2−i200000000−i2i2−i2i20000000000
χ31222-2-2-22-222-2-22000-2-220002-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-2200000-22−i2i2−i2i200000000i2−i2i2−i20000000000
χ32222-2-2-22-222-2-22000-2-220002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-2000002-2−i2i2−i2i200000000−i2i2−i2i20000000000
χ33222-2-2-22-222-2-2-200022-2000-2200i2i2−i2−i2i2i2−i2−i222−2−2−2−2220002i−2i2i−2i00−i2i2−i2i2000000002−2−220000000000
χ34222-2-2-22-222-2-2-200022-2000-2200i2i2−i2−i2i2i2−i2−i2−2−22222−2−2000−2i2i−2i2i00−i2i2−i2i200000000−222−20000000000
χ35222-2-2-22-222-2-2-200022-2000-2200−i2−i2i2i2−i2−i2i2i222−2−2−2−222000−2i2i−2i2i00i2−i2i2−i2000000002−2−220000000000
χ36222-2-2-22-222-2-2-200022-2000-2200−i2−i2i2i2−i2−i2i2i2−2−22222−2−20002i−2i2i−2i00i2−i2i2−i200000000−222−20000000000
χ37222-2-2-22-2-2-2222000-2-22000-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-22000002-2i2−i2−i2i200000000−i2i2−i2i20000000000
χ38222-2-2-22-2-2-2222000-2-22000-2200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-200000-22i2−i2−i2i200000000i2−i2i2−i20000000000
χ39222-2-2-22-2-2-2222000-2-22000-2200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-200000-22−i2i2i2−i200000000−i2i2−i2i20000000000
χ40222-2-2-22-2-2-2222000-2-22000-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-22000002-2−i2i2i2−i200000000i2−i2i2−i20000000000
χ41222-2-2-22-2-2-222-200022-20002-200i2i2−i2−i2−i2−i2i2i222−2−2−2−2220002i−2i−2i2i00−i2i2i2−i200000000−222−20000000000
χ42222-2-2-22-2-2-222-200022-20002-200i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000−2i2i2i−2i00−i2i2i2−i2000000002−2−220000000000
χ43222-2-2-22-2-2-222-200022-20002-200−i2−i2i2i2i2i2−i2−i222−2−2−2−222000−2i2i2i−2i00i2−i2−i2i200000000−222−20000000000
χ44222-2-2-22-2-2-222-200022-20002-200−i2−i2i2i2i2i2−i2−i2−2−22222−2−20002i−2i−2i2i00i2−i2−i2i2000000002−2−220000000000
χ452-222-22-2-2000022-2-22-2-222-20000000000002-22-22-22-200000000000002i2i−2i−2i000000002i−2i00000000
χ462-222-22-2-2000022-2-22-2-222-20000000000002-22-22-22-20000000000000−2i−2i2i2i00000000−2i2i00000000
χ472-222-22-2-2000022-2-22-2-222-2000000000000-22-22-22-2200000000000002i2i−2i−2i00000000−2i2i00000000
χ482-222-22-2-2000022-2-22-2-222-2000000000000-22-22-22-220000000000000−2i−2i2i2i000000002i−2i00000000
χ492-222-22-2-20000-2-222-222-22-20000000000002i−2i2i−2i−2i2i−2i2i0000000000000000022-2-20000002i−2i000000
χ502-222-22-2-20000-2-222-222-22-20000000000002i−2i2i−2i−2i2i−2i2i00000000000000000-2-222000000−2i2i000000
χ512-222-22-2-20000-2-222-222-22-2000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000022-2-2000000−2i2i000000
χ522-222-22-2-20000-2-222-222-22-2000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000-2-2220000002i−2i000000
χ532-2-2-2222-22-22-2022-2000-200002-22i−2i2i−2i2i−2i2i−2i0000000000000000000002−22−22−22−200000000i2−i2i2−i200
χ542-2-2-2222-22-22-2022-2000-200002-22i−2i2i−2i2i−2i2i−2i000000000000000000000−22−22−22−2200000000−i2i2−i2i200
χ552-2-2-2222-22-22-2022-2000-200002-2−2i2i−2i2i−2i2i−2i2i0000000000000000000002−22−22−22−200000000−i2i2−i2i200
χ562-2-2-2222-22-22-2022-2000-200002-2−2i2i−2i2i−2i2i−2i2i000000000000000000000−22−22−22−2200000000i2−i2i2−i200
χ572-2-2-2222-2-22-22022-2000-20000-222i−2i2i−2i−2i2i−2i2i0000000000000000000002−22−2−22−2200000000i2−i2−i2i200
χ582-2-2-2222-2-22-22022-2000-20000-222i−2i2i−2i−2i2i−2i2i000000000000000000000−22−222−22−200000000−i2i2i2−i200
χ592-2-2-2222-2-22-22022-2000-20000-22−2i2i−2i2i2i−2i2i−2i0000000000000000000002−22−2−22−2200000000−i2i2i2−i200
χ602-2-2-2222-2-22-22022-2000-20000-22−2i2i−2i2i2i−2i2i−2i000000000000000000000−22−222−22−200000000i2−i2−i2i200
χ6144-4-4-44-44000004-44000-4000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ6244-4-4-44-44000004-44000-400000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ6344-4-4-44-4400000-44-4000400000000000000000000000000000000000000022−22−222200000000000000
χ6444-4-4-44-4400000-44-40004000000000000000000000000000000000000000−222222−2200000000000000
χ654-444-44-4-400004-4444-4-4-4-440000000000000000000000000000000000000000000000000000000
χ664-444-44-4-40000-44-4-4-4444-440000000000000000000000000000000000000000000000000000000
χ674-44-44-4-4400004000-44-40000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ684-44-44-4-4400004000-44-4000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ694-44-44-4-440000-40004-4400000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ704-44-44-4-440000-40004-44000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ714-4-44-4-4444-4-440000000000000022−22−222222−22−22220000000000000000000000000000000000000000000
χ724-4-44-4-4444-4-4400000000000000−222222−22−222222−220000000000000000000000000000000000000000000
χ734-4-44-4-444-444-40000000000000022−22−2222−222222−220000000000000000000000000000000000000000000
χ744-4-44-4-444-444-400000000000000−222222−2222−22−22220000000000000000000000000000000000000000000
χ754-4-4-4444-44-44-40-4-4400040000-44000000000000000000000000000000000000000000000000000
χ764-4-4-4444-4-44-440-4-44000400004-4000000000000000000000000000000000000000000000000000
χ7788-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).